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Time-consistent approximations of risk-averse multistage stochastic optimization problems

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In this paper we study the concept of time consistency as it relates to multistage risk-averse stochastic optimization problems on finite scenario trees. We use dynamic time-consistent formulations to approximate problems having a single coherent risk measure applied to the aggregated costs over all time periods. The dual representation of coherent risk measures is used to create a time-consistent cutting plane algorithm. Additionally, we also develop methods for the construction of universal time-consistent upper bounds, when the objective function is the mean-semideviation measure of risk. Our numerical results indicate that the resulting dynamic formulations yield close approximations to the original problem.

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Authors and Affiliations

  1. Department of Operations Research and Financial Engineering, Princeton University, Princeton, NJ, 08544, USA

    Tsvetan Asamov

  2. Department of Management Science and Information Systems, Rutgers University, 94 Rockefeller Road, Piscataway, NJ, 08854, USA

    Andrzej Ruszczyński

Authors
  1. Tsvetan Asamov
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  2. Andrzej Ruszczyński
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Correspondence to Andrzej Ruszczyński.

Additional information

This work was supported by the Air Force Office of Scientific Research (award FA9550-11-1-0164), and by the National Science Foundation (award DMS-1312016).

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Asamov, T., Ruszczyński, A. Time-consistent approximations of risk-averse multistage stochastic optimization problems. Math. Program. 153, 459–493 (2015). https://doi.org/10.1007/s10107-014-0813-x

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  • DOI: https://doi.org/10.1007/s10107-014-0813-x

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